A272727 a(0)=0; thereafter a(n+1) is the number of coincidences between the sequence so far (a(0), ..., a(n)) and its reverse (a(n), ..., a(0)).

0, 1, 0, 3, 0, 3, 0, 5, 0, 7, 0, 7, 0, 7, 0, 9, 0, 9, 0, 11, 0, 13, 0, 15, 0, 15, 0, 15, 0, 15, 0, 17, 0, 19, 0, 19, 0, 19, 0, 21, 0, 21, 0, 23, 0, 23, 0, 25, 0, 27, 0, 29, 0, 31, 0, 31, 0, 31, 0, 31, 0, 31, 0, 33, 0, 33, 0, 35, 0, 37, 0, 39, 0, 39, 0, 39, 0, 39, 0, 41, 0, 43

Offset: 0

Author

Ivan Neretin, May 05 2016

Keywords

• nonn

Comments

a(2n-1) is positive and odd.

a(2n+1) - a(2n-1) is always either 0 or 2.

The number of repetitions of the value 2n-1 is A272729(n).

Examples

			A one-element series [0] coincides with its own reverse, hence a(1)=1.
[0,1] and [1,0] differ in every term, hence a(2)=0.
[0,1,0] is its own reverse, hence a(3)=3.
[0,1,0,3] and [3,0,1,0] differ in every term, hence a(4)=0.
[0,1,0,3,0] and [0,3,0,1,0] coincide in three terms, hence a(5)=3.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A272728, A272729.

Programs

Mathematica

Nest[Append[#, Count[# - Reverse[#], x_ /; x == 0]] &, {0}, 81]

Formula

a(2n)=0.

a(2n-1)=A272728(n)+n.